{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:34:44Z","timestamp":1760146484684,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2024,11,3]],"date-time":"2024-11-03T00:00:00Z","timestamp":1730592000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Projects of Talents Recruitment of GDUPT","award":["2022rcyj2012","2023KTSCX089","2024063"],"award-info":[{"award-number":["2022rcyj2012","2023KTSCX089","2024063"]}]},{"name":"Characteristic Innovation Project of Guangdong Province Ordinary University","award":["2022rcyj2012","2023KTSCX089","2024063"],"award-info":[{"award-number":["2022rcyj2012","2023KTSCX089","2024063"]}]},{"name":"Maoming Science and technology projects","award":["2022rcyj2012","2023KTSCX089","2024063"],"award-info":[{"award-number":["2022rcyj2012","2023KTSCX089","2024063"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We addressed the Ulam stability of second-order periodic linear differential equations with periodic damping. The necessary and sufficient conditions for the Ulam stability of second-order periodic linear differential equations were obtained by providing an Ulam stability theorem and an Ulam instability theorem. In particular, when the elastic coefficient remained constant at 0, a very general conclusion was obtained. These results expand on the conclusions in the relevant literature. In addition, for the situation of constant coefficients, the minimum Ulam constant is provided.<\/jats:p>","DOI":"10.3390\/sym16111459","type":"journal-article","created":{"date-parts":[[2024,11,4]],"date-time":"2024-11-04T03:57:34Z","timestamp":1730692654000},"page":"1459","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Ulam Stability of Second-Order Periodic Linear Differential Equations with Periodic Damping"],"prefix":"10.3390","volume":"16","author":[{"given":"Jin","family":"Li","sequence":"first","affiliation":[{"name":"College of Science, Guangdong University of Petrochemical Technology, Maoming 525000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaofang","family":"Xia","sequence":"additional","affiliation":[{"name":"Library, Guangdong University of Petrochemical Technology, Maoming 525000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chuanfang","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Science, Guangdong University of Petrochemical Technology, Maoming 525000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Renlian","family":"Chen","sequence":"additional","affiliation":[{"name":"College of Science, Guangdong University of Petrochemical Technology, Maoming 525000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,3]]},"reference":[{"key":"ref_1","unstructured":"Ulam, S.M. 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Ulam stability for a class of Hill\u2019s equations. Symmetry, 11.","DOI":"10.3390\/sym11121483"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"C\u01cedariu, L., Popa, D., and Ra\u015fa, I. (2020). Ulam stability of a second linear differential operator with nonconstant coefficients. Symmetry, 12.","DOI":"10.3390\/sym12091451"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"553","DOI":"10.22199\/issn.0717-6279-2019-03-0035","article-title":"Hyers-Ulam stability of nth order linear differential equation","volume":"38","author":"Murali","year":"2019","journal-title":"Proyecciones"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"579","DOI":"10.5937\/KgJMath1804579M","article-title":"Hyers-Ulam-Rassias stability for the linear ordinary differential equation of third order","volume":"42","author":"Murali","year":"2018","journal-title":"Kragujevac J. 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Lett."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/11\/1459\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:27:38Z","timestamp":1760113658000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/11\/1459"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,3]]},"references-count":19,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2024,11]]}},"alternative-id":["sym16111459"],"URL":"https:\/\/doi.org\/10.3390\/sym16111459","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2024,11,3]]}}}